Andersen Group El.-Phon. QMC C60 Resistivity saturation

Alkali-doped fullerenes

For the nonexperts some general information about fullerenes, a brief description of our early work in German and a link to Encyclopaedia Britannica have been included.

Alkali-doped C60 compounds, AnC60 (A= K, Rb), are characterized by an unusual parameter range, which leads to interesting properties and a challenging test of theoretical methods. Furthermore, many A3C60 compounds are superconductors, with a critical temperature Tc which is only exceeded by cuprates. This has raised question about whether these systems are conventional superconductors.

Important parameters for fullerides are the effective Coulomb repulsion U between two electrons on the same molecule, the one-electron band width W of the partly occupied t1u band, the maximum phonon frequency wph, the Jahn-Teller energy EJT and the exchange integral K. Typical estimates of these parameters are

U 1.0-1.5 eV
W 0.6 eV
wph 0.2 eV
EJT 0.1 eV
K 0.1 eV

This leads to interesting questions:
1. Since U>W, one might have expected all AnC60 compounds to be insulators, while experimentally A3C60 are metals and A4C60 are insulators.
2. Migdal's theorem plays an important role in the theory of conventional superconductors. Since, however, wph is similar to W, it is questionable if this theorem is valid for the fullerides.
3. The superconductivity is driven by the electron-phonon interaction, which induces an attractive interaction of the order 0.1 eV. At the same time there is a repulsive Coulomb repulsion U of the order 1 to 1.5 eV. In conventional superconductors this repulsion is believed to be drastically reduced by retardation effects, due to the vastly different energy scales of the electrons and phonons. Here wph and W are comparable, which raises basic questions about why superconductivity is at all possible.
4. For large temperatures the resistivity becomes very large and the corresponding mean free path much shorter than the separation between two molecules. This raises interesting questions about the interpretation and whether such a result is even possible. The unusual resistivity is related to the small band width.
5. There is an interesting competition between the Jahn-Teller effect, the Hund's rule coupling, the kinetic and the Coulomb energies.

Since these issues emphasize the many-body nature of the problem and since AnC60 is very complicated, our work is mainly based on model calculations. For this purpose we have constructed appropriate models and determined the corresponding parameters from ab initio calculations or experiments. The models are solved by using Quantum Monte-Carlo (T=0 projection and finite T determinantal) methods, dynamical mean-field theory or exact diagonalization techniques.

Among the issues treated are:
Models and parameters
Metal-insulator transition
Electron-phonon interaction
Coulomb pseudopotential
Jahn-Teller effect
Orientational interaction
Electronic structure
Optical conductivity
Raman scattering
Electron density of states
Fullerene molecules

Properties of A3C60 have been discussed extensively in the book "Alkali-doped Fullerides. Narrow-band solids with unusual properties" ( World Scientific, Singapore, 2004. XVII, 282 p., hardcover. ISBN 981-238-667-X ). Also available at Amazon.

Superconductivity properties have been reviewed in "Superconductivity in Fullerides" ( Rev. Mod. Phys. 69, 575 (1997)).

A list of some relevant publications is given.

For further information contact Olle Gunnarsson ( or Erik Koch (

Last Update: October 2010

Max-Planck Institut für Festkörperforschung
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Andersen Group Max-Planck-Institut für Festkörperforschung
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